Collisional Energy Loss Research Articles

Constraining heavy quark energy loss using B and D meson measurements in heavy ion collision at RHIC and LHC energies

In this work, we calculate energy loss of heavy quark (charm and bottom) due to elastic collisions and gluon radiation in hot/dense medium. The collisional energy loss has been obtained using QCD calculations. The radiative energy loss is calculated using reaction operator formalism and generalized dead cone approach. We rederive the energy loss expression using same assumptions as generalized dead cone approach but obtain slightly different results. We also improve the model employed to calculate path length and the system evolution. The nuclear modification factors RAA including shadowing and energy loss are evaluated for B and D mesons and are compared with the measurements in PbPb collision at sNN=2.76 TeV and with the D meson and Heavy flavor (HF) electrons measurements in AuAu collision at sNN=200 GeV. The radiative energy loss calculated by reaction operator formalism added with collisional energy loss describes the RHIC HF electron suppression in high pT range. It also describes the LHC measurement of B meson suppression but overestimates the suppression of D meson. The radiative energy loss from generalized dead cone approach describes the charm suppression at both RHIC as well as LHC energies and requires energy loss due to collisions to be added in order to describe the bottom suppression at LHC.

Updated analytical solutions of continuity equation for electron beams precipitation – I. Pure collisional and pure ohmic energy losses

We present updated analytical solutions of continuity equations for power-law beam electrons precipitating in (a) purely collisional losses and (b) purely ohmic losses. The solutions of continuity equation (CE) normalized on electron density presented in Dobranskis & Zharkova are found by method of characteristics eliminating a mistake in the density characteristic pointed out by Emslie et al. The corrected electron beam differential densities (DD) for collisions are shown to have energy spectra with the index of −(γ + 1)/2, coinciding with the one derived from the inverse problem solution by Brown, while being lower by 1/2 than the index of −γ/2 obtained from CE for electron flux. This leads to a decrease of the index of mean electron spectra from −(γ − 2.5) (CE for flux) to −(γ − 2.0) (CE for electron density). The similar method is applied to CE for electrons precipitating in electric field induced by the beam itself. For the first time, the electron energy spectra are calculated for both constant and variable electric fields by using CE for electron density. We derive electron DD for precipitating electrons (moving towards the photosphere, μ = +1) and ‘returning’ electrons (moving towards the corona, μ = −1). The indices of DD energy spectra are reduced from −γ − 1 (CE for flux) to −γ (CE for electron density). While the index of mean electron spectra is increased by 0.5, from −γ + 0.5 (CE for flux) to −γ + 1(CE for electron density). Hard X-ray intensities are also calculated for relativistic cross-section for the updated differential spectra revealing closer resemblance to numerical Fokker–Planck (FP) solutions.

A semi-holographic model for heavy-ion collisions

We develop a semi-holographic model for the out-of-equilibrium dynamics during the partonic stages of an ultrarelativistic heavy-ion collision. The model combines a weakly-coupled hard sector, involving gluon modes with energy and momenta of the order of the saturation momentum and relatively large occupation numbers, with a strongly-coupled soft sector, which physically represents the soft gluons radiated by the hard partons. The hard sector is described by perturbative QCD, more precisely, by its semi-classical approximation (the classical Yang-Mills equations) which becomes appropriate when the occupation numbers are large. The soft sector is described by a marginally deformed conformal field theory, which in turn admits a holographic description in terms of classical Einstein's equations in $AdS_5$ with a minimally coupled massless `dilaton'. The model involve two free parameters which characterize the gauge-invariant couplings between the hard and soft sectors. Via these couplings, the hard modes provide dynamical sources for the gravitational equations at the boundary of $AdS_5$ and feel the feedback of the latter as additional soft sources in the classical Yang-Mills equations. Importantly, the initial conditions for this coupled dynamics are fully determined by the hard sector alone, i.e. by perturbative QCD, and are conveniently given by the color glass condensate (CGC) effective theory. We also develop a new semi-holographic picture of jets in the QGP by attaching a non-Abelian charge to the endpoint of the trailing string in $AdS_5$ representing a heavy quark. This leads to modified Nambu-Goto equations for the string which govern the (collisional and radiative) energy loss by the heavy quark towards both hard and soft modes.

Importance of different energy loss effects in jet suppression at the RHIC and the LHC

Jet suppression is considered to be an excellent probe of quantum chromodynamic (QCD) matter created in ultra-relativistic heavy ion collisions. Our theoretical predictions of jet suppression, which are based on our recently developed dynamical energy loss formalism, show a robust agreement with various experimental data, which spans across different probes, experiments (Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC)) and experimental conditions (i.e. all available centrality regions). This formalism includes several key ingredients, such as the inclusion of dynamical scattering centers, a finite size QCD medium, collisional energy loss, finite magnetic mass and running coupling. While these effects have to be included based on theoretical grounds, it is currently unclear what their individual importance is in accurately interpreting the experimental data; in particular because other approaches to suppression predictions commonly neglect some—or all—of these effects. To address this question, we study the relative importance of these effects in obtaining accurate suppression predictions for D mesons (clear energy loss probe) at top RHIC and LHC energies. We obtain that several different ingredients are responsible for accurate predictions, i.e. robust agreement with the data is a cumulative effect of all the ingredients, though inclusion of the dynamical scattering centers has the largest relative importance.

Analysis of the Quark-Gluon Plasma by Heavy Quarks

We discuss the present status of the tomography of a quark gluon plasma (QGP) with help of heavy quarks. We address the question whether collisional or radiative energy loss dominates, how different expansion scenarios of the medium influence the observables and which state of the expansion is impressed in the RAA and v2 observables.

Energy loss in jet suppression - what effects matter?

Jet suppression is considered to be an excellent probe of QCD matter created in ultra-relativistic heavy ion collisions. Our theoretical predictions of jet suppression, based on our recently developed dynamical energy loss formalism, show a robust agreement with various experimental data for different probes, experiments (RHIC and LHC) and centrality regions. Our dynamical energy loss formalism includes the following key ingredients: dynamical scattering centers, collisional energy loss, finite magnetic mass and running coupling. Although all these ingredients are theoretically justified, it is currently unclear how they individually contribute to accurate suppression predictions. Natural question rises: is there one effect which is crucial for the agreement, or is the agreement a joint effect of several smaller improvements. To answer this question, we study how the above mentioned key effects affect the suppression calculations. Our results show that each energy loss effect is important and that a robust agreement between theoretical predictions and experimental data is a cumulative effect of all improvements.

Measurements of jets in ALICE

Partonic energy loss in the medium formed in heavy ion collisions results in significant modifications of jet spectra. Quantitative understanding of these modifications can constrain models for partonic energy loss in heavy ion collisions. The ALICE detector is capable of unique measurements of jets due to its low momentum tracking and particle identification capabilities. The ALICE Electromagnetic Calorimeter (EMCAL) is a key element for the measurement of fully reconstructed jets in ALICE due to its measurement of neutral particles and its triggering capabilities. Measurements of fully reconstructed jet spectra and the nuclear modification factor, RAA, in Pb-Pb collisions at = 2.76 TeV are presented.

Stratification of discharge in noble gases from the viewpoint of the discrete dynamics

Based on the analysis of electron phase trajectories in sinusoidal electric fields, a new point of view on discharge stratification is proposed. It is shown that the positive column can be considered as a spatial resonator in which electric fields with a fundamental period length LS or higher mode length qpLS establish, where p and q are integers and p > q. The fundamental mode length LS is equivalent to the distance on which electrons gain energy equal to the lowest excitation threshold. This distance determines a length of the S-striation. Unlike kinetic theory, in the presented model resonance properties of the discharge column are not connected with elastic collision energy losses. A point map is used to obtain the resonance trajectories of electrons in the phase plane. Stable points for the positions of inelastic collisions in the resonance trajectories have been found at the positions of field maxima in the case of integer ratios pq. For non-integer ratios pq, multiple resonance trajectories arise according to a more complex stability criterion. From this point of view, S-, P-, and R-striations in noble gas discharges can be explained. Due to energy losses in elastic collisions, initial electron energy distribution functions converge to the resonance trajectories (the so-called “bunch effect”). The findings of the discrete model agree with results of kinetic theory and experiment. The new approach avoids difficulties of the kinetic theory in the case of exceptionally large relaxation lengths which can even exceed the positive column length.

Nuclear suppression of muons at forward rapidity at relativistic heavy ion collisions

Heavy quarks produced in the initial stage of heavy ion collisions would traverse the quark gluon plasma, colliding with quarks and gluons and radiating gluons. In the process of collision with the quarks and gluons and also by radiation of gluons they lose energy. After their production, they may get fragmented into heavy mesons by picking up light quarks/antiquarks and in turn may decay through leptonic channels. These leptons would carry information of the initial stage of heavy ion collisions and also the evolution of the plasma. In this work, we have made a detailed study for the nuclear modification factor of production of muons from the initial fusion of partons in a nuclear collision at LHC energy. We also present our result for the azimuthal anisotropy of heavy quark decay muons at LHC energy. We consider both the radiative and collision energy loss along with longitudinal expansion of the plasma for these calculations. We compare our results of muon RAA for Pb+Pb collisions at 2.76 ATeV with ALICE data and results of muon v2 for Pb+Pb collisions at 2.76 ATeV with ALICE preliminary data.

Energy loss straggling of (0.5 < Ep < 2.0) MeV protons in formvar

Energy loss distributions for (0.5<Ep<2.0)MeV protons traversing polyvinyl formal have been measured in transmission. Then, they have been analyzed in order to determine energy loss straggling variance data. For avoiding non-stochastic broadenings and single collision events, only energy loss fractions within the range 2%⩽ΔEE⩽20% have been considered. The inferred energy loss straggling data are compared to values derived by several theories of the collisional energy straggling and by Yang et al. empirical formula with assuming the validity of the Bragg–Kleeman additivity rule for compounds in all the performed calculations. The obtained results are discussed with distinguishing two projectile velocity regimes delimited by the proton energy Ep∼1.2MeV. Over the high proton velocity regime, our data are in very consistent with the classical Bohr theory and the Yang et al. empirical formula predicting constant collisional energy loss straggling. It clearly appears that over the low proton velocity regime, our energy loss straggling data are in best overall quantitative agreement with values predicted by the Sigmund–Schinner binary collision stopping theory (the BCAS) involving both the shell and Barkas–Anderson corrections. Besides, the slight low energy-dependent behavior of experimental data shows to be consistent with the predictions of the Bethe–Livingston theory and the Yang et al. empirical formula.

Subharmonic Response of Linear Vibroimpact System with Fractional Derivative Damping to a Randomly Disrobed Periodic Excitation

The subharmonic response of single-degree-of-freedom vibroimpact oscillator with fractional derivative damping and one-sided barrier under narrow-band random excitation is investigated. With the help of a special Zhuravlev transformation, the system is reduced to one without impacts, thereby permitting the applications of asymptotic averaging over the period for slowly varying random process. The analytical expression of the response amplitude is obtained in the case without random disorder, while only the approximate analytical expressions for the steady-state moments of the response amplitude are obtained in the case with random disorder. The effects of the fractional order derivative term, damping term, random disorder, and the coefficient of restitution and other system parameters on the system response are discussed. Theoretical analyses and numerical simulations show that fractional derivative makes both the system damping and stiffness coefficients increase, such that it changes the system parameters region at which the response amplitude reaches the maximum. The system energy loss in collision is equivalent to increasing the damping coefficient of the system. System response amplitude will increase when the excitation frequency is close to the resonant frequency and will decay rapidly when the excitation frequency gradually deviates from the resonance frequency.

Effect of the electron energy distribution on total energy loss with argon in inductively coupled plasmas

The total energy lost per electron-ion pair lost εT is investigated with the electron energy distribution function (EEDF). The EEDFs are measured at various argon powers in RF inductively coupled plasma, and the EEDFs show a depleted distribution (a discontinuity occurring at the minimum argon excitation threshold energy level) with the bulk temperature and the tail temperature. The total energy loss per electron-ion pair lost εT is calculated from a power balance model with the Maxwellian EEDFs and the depleted EEDFs and then compared with the measured εT from the floating probe. It is concluded that the small population of the depleted high energy electrons dramatically increases the collisional energy loss, and the calculated εT from the depleted EEDFs has a value that is similar to the measured εT.

Dynamical collisional energy loss and transport properties of on- and off-shell heavy quarks in vacuum and in the quark gluon plasma

In this study we evaluate the dynamical collisional energy loss of heavy quarks, their interaction rate, as well as the different transport coefficients (drag and diffusion coefficients, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$, etc). We calculate these different quantities for (i) perturbative partons (on-shell particles in the vacuum with fixed and running coupling) and (ii) for dynamical quasi-particles (off-shell particles in the QGP medium at finite temperature $T$ with a running coupling in temperature as described by the dynamical quasiparticles model). We use the perturbative elastic $[q(g)Q\ensuremath{\rightarrow}q(g)Q]$ cross section for the first case and the infrared enhanced hard thermal loop cross sections for the second. The results obtained in this work demonstrate the effects of a finite parton mass and width on the heavy-quark transport properties and provide the basic ingredients for an explicit study of the microscopic dynamics of heavy flavors in the QGP--as formed in relativistic heavy-ion collisions--within transport approaches developed previously by the authors.

Heavy flavor dynamics in QGP and hadron gas

We study heavy flavor evolution in the quark-gluon plasma matter and the subsequent hadron gas created in ultrarelativistic heavy-ion collisions. The motion of heavy quarks inside the QGP is described using our modified Langevin framework that incorporates both collisional and radiative energy loss mechanisms; and the scatterings between heavy mesons and the hadron gas are simulated with the UrQMD model. We find that the hadronic interaction further suppresses the $D$ meson $R_\mathrm{AA}$ at high $p_\mathrm{T}$ and enhances its $v_2$. And our calculations provide good descriptions of experimental data from both RHIC and LHC. In addition, we explore the heavy-flavor-tagged angular correlation functions and find them to be a potential candidate for distinguishing different energy loss mechanisms of heavy quarks inside the QGP.

Medical radiation dosimetry—theory of charged particle collision energy loss by Brain McParland

Medical radiation dosimetry—theory of charged particle collision energy loss by Brain McParland

RHIC and LHC jet suppression in non-central collisions

Understanding properties of QCD matter created in ultra-relativistic heavy-ion collisions is a major goal of RHIC and LHC experiments. An excellent tool to study these properties is high-momentum hadron suppression of light and heavy flavor observables. Utilizing this tool requires accurate suppression predictions for different experiments, probes and experimental conditions, and their unbiased comparison with experimental data. With this goal, we here extend our dynamical energy loss formalism towards generating predictions for non-central collisions; the formalism takes into account both radiative and collisional energy loss, dynamical (as opposed to static) scattering centers, finite magnetic mass, running coupling and uses no free parameters in comparison with experimental data. Specifically, we here generate predictions for all available centrality ranges, for both LHC and RHIC experiments, and for four different probes (charged hadrons, neutral pions, D mesons and non-prompt J/ψ). We obtain good agreement with all available non-central data, and also generate predictions for suppression measurements that will soon become available. Finally, we discuss implications of the obtained good agreement with experimental data with different medium models that are currently considered.

Gluon radiation by heavy quarks at intermediate energies and consequences for the mass hierarchy of energy loss

We extend the Gunion Bertsch calculation of gluon radiation in single scattering to the case of finite mass quarks. This case applies to the radiative energy-loss of heavy quarks of intermediate energies propagating in a quark gluon plasma. We discuss more specifically the dead cone effect as well as the mass hierarchy of the collisional and radiative energy loss and provide some predictions for observables sensitive to the mass hierarchy of energy loss in ultrarelativistic heavy ion collisions.

Dynamical evolution, hadronization and angular de-correlation of heavy flavor in a hot and dense QCD medium

We study heavy flavor evolution and hadronization in relativistic heavy-ion collisions. The in-medium evolution of heavy quarks is described using our modified Langevin framework that incorporates both collisional and radiative energy loss mechanisms. The subsequent hadronization process for heavy quarks is calculated with a fragmentation plus recombination model. We find significant contribution from gluon radiation to heavy quark energy loss at high $p_T$; the recombination mechanism can greatly enhance D meson production at medium $p_T$. Our calculation provides a good description of D meson nuclear modification at the LHC. In addition, we explore the angular correlation functions of heavy flavor pairs which may provide us a potential candidate for distinguishing different energy loss mechanisms of heavy quarks inside QGP.

Azimuthal correlations of heavy quarks in Pb + Pb collisions ats=2.76TeV at the CERN Large Hadron Collider

In this paper we study the azimuthal correlations of heavy quarks in Pb+Pb collisions with $\sqrt{s}=2.76$ TeV at LHC. Due to the interaction with the medium heavy quarks and antiquarks are deflected from their original direction and the initial correlation of the pair is broadened. We investigate this effect for different transverse momentum classes. Low-momentum heavy-quark pairs lose their leading order back-to-back initial correlation, while a significant residual correlation survives at large momenta. Due to the larger acquired average deflection from their original directions the azimuthal correlations of heavy-quark pairs are broadened more efficiently in a purely collisional energy loss mechanism compared to including radiative corrections. This discriminatory feature survives when next-to-leading order production processes are included.

ON THE SOLUTION OF THE CONTINUITY EQUATION FOR PRECIPITATING ELECTRONS IN SOLAR FLARES

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an updated exact analytical to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the new analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.